3 Answers
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IS modes are used to tell the camera what kind of movement to correct for. All implementations I'm aware of have at least two modes: "normal" to correct for motion in all axes and "panning" to allow motion in one axis while correcting for motion in the other.

The exact details of each available mode depend on the manufacturer, for example Canon lenses can have up to three modes (normal, panning, and panning but only active when taking the shot), while Nikon lenses only have two modes (on when focusing, on when taking the shot) but panning detection is automatic rather than by changing modes and they also offer a choice of two motion correction modes 'Normal' and 'Active', with Active being intended for use while in a moving vehicle and therefore offering stronger correction.

Newer lenses will generally have more IS modes available than older lenses, and stabilized Telephoto (and Super-Telephoto lenses) will usually have more modes than stabilized primes or zooms.

The IS in newer lenses will also tend to be more effective than in older lenses allowing for even lower shutter speeds.

All newish Canon lenses have two IS modes, normal (Mode 1) and panning (Mode 2). Basically you use normal for everything except when you're panning to capture "motion" in the picture. The same is true for the Sigma lens I've tried.